On a Relationship between Completely Separating Systems and Antimagic Labeling of Regular Graphs

  • Oudone Phanalasy
  • Mirka Miller
  • Leanne Rylands
  • Paulette Lieby
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


A completely separating system (CSS) on a finite set [n] is a collection \(\mathcal C\) of subsets of [n] in which for each pair a ≠ b ∈ [n], there exist \(A, B\in\mathcal C\) such that a ∈ A, b ∉ A and b ∈ B, a ∉ B.

An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers {1,2, ..., q} such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling.

In this paper we show that there is a relationship between CSSs on a finite set and antimagic labeling of graphs. Using this relationship we prove the antimagicness of various families of regular graphs.


completely separating system vertex antimagic edge labeling antimagic labeling regular graph 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Oudone Phanalasy
    • 1
    • 2
  • Mirka Miller
    • 1
    • 3
    • 4
    • 5
  • Leanne Rylands
    • 6
  • Paulette Lieby
    • 7
  1. 1.School of Electrical Engineering and Computer ScienceThe University of NewcastleAustralia
  2. 2.Department of MathematicsNational University of LaosVientianeLaos
  3. 3.Department of MathematicsUniversity of West BohemiaPilsenCzech Republic
  4. 4.Department of Computer ScienceKing’s College LondonUK
  5. 5.Department of MathematicsITB BandungIndonesia
  6. 6.School of Computing and MathematicsUniversity of Western SydneyAustralia
  7. 7.NICTACanberraAustralia

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